Problem: Divide the following complex numbers: $\dfrac{2 e^{19\pi i / 12}}{ e^{5\pi i / 4}}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Explanation: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $2 e^{19\pi i / 12}$ ) has angle $\frac{19}{12}\pi$ and radius 2. The second number ( $ e^{5\pi i / 4}$ ) has angle $\frac{5}{4}\pi$ and radius 1. The radius of the result will be $\frac{2}{1}$ , which is 2. The angle of the result is $\frac{19}{12}\pi - \frac{5}{4}\pi = \frac{1}{3}\pi$ The radius of the result is $2$ and the angle of the result is $\frac{1}{3}\pi$.